Finite Group Databasebeta

← C151×#18731 #50323656

Subgroups — C151×#18731 #50323656

Order 38656.

884 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 884 conjugacy classes of subgroups — too many to draw. Only its 230 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#3556×C151C211yesmaximal, characteristic, complemented
2#3208×C151C212yesmaximal
3#3138×C151C211yesmaximal, characteristic
4#1626×C151C218yesmaximal, complemented
5#1544×C151C211yesmaximal, characteristic, complemented
6#1485×C151C212yesmaximal, complemented
7#564×C151—22no—
8#557×C151—22no—
9#557×C151—22no—
10#557×C151C2214yescomplemented
11#541×C151—24no—
12#541×C151—22no—
13#533×C151C2212yes—
14#533×C151C2211yescharacteristic
15C2×#127×C151C2211yescharacteristic
16#492×C151—22no—
17#490×C151—22no—
18#486×C151—22no—
19#486×C151C2214yes—
20#460×C151C2218yes—
21#450×C151—24no—
22#431×C151C2212yes—
23#418×C151—22no—
24C4×M16×C151C2211yescharacteristic
25#332×C151C2214yescomplemented
26Q8⋊C8×C151C2218yescomplemented
27C22×D4×C151—21no—
28C22×D4×C151—22no—
29C2×SD16×C151—28no—
30C2×M16×C151—21no—
31C4⋊Q8×C151—22no—
32C4⋊Q8×C151—24no—
33C4⋊Q8×C151D412yes—
34C4⋊Q8×C151D412yes—
35C4⋊Q8×C151C2312yes—
36#127×C151—22no—
37#127×C151—21no—
38#127×C151C2312yes—
39#126×C151—28no—
40#125×C151—22no—
41#125×C151—28no—
42#125×C151—28no—
43#125×C151—24no—
44#125×C151—28no—
45#125×C151—22no—
46#125×C151D412yes—
47C22⋊Q8×C151—22no—
48C22⋊Q8×C151—22no—
49C22⋊Q8×C151D414yes—
50C4×Q8×C151—24no—
51C4×Q8×C151—24no—
52C4×Q8×C151—22no—
53C4×Q8×C151—22no—
54C4×Q8×C151—24no—
55C4×Q8×C151C2314yes—
56#117×C151—22no—
57#117×C151D412yes—
58C2×C42×C151C2311yescharacteristic
59C4⋊C8×C151C2314yes—
60#102×C151—28no—
61#102×C151—28no—
62C22⋊C8×C151—22no—
63#97×C151—21no—
64C4×C8×C151—22no—
65C4×C8×C151C2312yes—
66C24×C151—41no—
67C2×Q8×C151—22no—
68C2×Q8×C151—22no—
69C2×Q8×C151C2×D414yes—
70C2×D4×C151—22no—
71C2×D4×C151—24no—
72C2×D4×C151—44no—
73C2×D4×C151—42no—
74C2×D4×C151—41no—
75C2×D4×C151—84no—
76C22×C4×C151C2×D412yes—
77C22×C4×C151C2×D411yescharacteristic
78SD16×C151—88no—
79M16×C151—42no—
80C2×C8×C151—24no—
81C2×C8×C151—22no—
82C4⋊C4×C151—28no—
83C4⋊C4×C151—28no—
84C4⋊C4×C151—28no—
85C4⋊C4×C151—22no—
86C4⋊C4×C151—22no—
87C4⋊C4×C151—22no—
88C4⋊C4×C151—24no—
89C4⋊C4×C151—24no—
90C4⋊C4×C151—22no—
91C4⋊C4×C151—24no—
92C4⋊C4×C151C2×D414yes—
93C4⋊C4×C151C2×D414yes—
94C22⋊C4×C151—24no—
95C22⋊C4×C151—22no—
96C42×C151—28no—
97C42×C151—22no—
98C42×C151—24no—
99C42×C151C2×D412yes—
100C42×C151C2×D411yescharacteristic
101C42×C151C2411yescharacteristic
102C23×C151—42no—
103C23×C151—82no—
104C23×C151—84no—
105C23×C151#12011yescharacteristic
106Q8×C151—28no—
107Q8×C151—44no—
108Q8×C151—44no—
109D4×C151—44no—
110D4×C151—48no—
111D4×C151—84no—
112D4×C151—82no—
113C2×C4×C151—24no—
114C2×C4×C151—22no—
115C2×C4×C151—24no—
116C2×C4×C151—24no—
117C2×C4×C151—24no—
118C2×C4×C151#12012yes—
119C2×C4×C151#12011yescharacteristic
120C2×C4×C151C22×D411yescharacteristic
121C2×C4×C151C22×D412yes—
122C8×C151—42no—
123C8×C151—44no—
124C22×C151—22no—
125C22×C151—21no—
126C22×C151—84no—
127C22×C151—82no—
128C22×C151—164no—
129C22×C151C2×#12011yescharacteristic
130C4×C151—22no—
131C4×C151—21no—
132C4×C151—44no—
133C4×C151—44no—
134C4×C151—44no—
135C4×C151#45412yes—
136C4×C151#57714yes—
137C2×C151—41no—
138C2×C151—162no—
139C2×C151#301012yes—
140C2×C151C2×#45411yescharacteristic
141#18731C15111yesmaximal, characteristic, direct product factor, Sylow
142C151#1873111yescharacteristic, direct product factor, Sylow
143#3556C2×C15111yescharacteristic, complemented
144#3208C2×C15112yes—
145#3138C2×C15111yescharacteristic
146#1626C2×C15118yescomplemented
147#1544C2×C15111yescharacteristic, complemented
148#1485C2×C15112yescomplemented
149#564—22no—
150#557—22no—
151#557—22no—
152#557C22×C15114yescomplemented
153#541—24no—
154#541—22no—
155#533C22×C15112yes—
156#533C22×C15111yescharacteristic
157C2×#127C22×C15111yescharacteristic
158#492—22no—
159#490—22no—
160#486—22no—
161#486C22×C15114yes—
162#460C22×C15118yes—
163#450—24no—
164#431C22×C15112yes—
165#418—22no—
166C4×M16C22×C15111yescharacteristic
167#332C22×C15114yescomplemented
168Q8⋊C8C22×C15118yescomplemented
169C22×D4—21no—
170C22×D4—22no—
171C2×SD16—28no—
172C2×M16—21no—
173C4⋊Q8—22no—
174C4⋊Q8—24no—
175C4⋊Q8D4×C15112yes—
176C4⋊Q8D4×C15112yes—
177C4⋊Q8C23×C15112yes—
178#127—22no—
179#127—21no—
180#127C23×C15112yes—
181#126—28no—
182#125—22no—
183#125—28no—
184#125—28no—
185#125—24no—
186#125—28no—
187#125—22no—
188#125D4×C15112yes—
189C22⋊Q8—22no—
190C22⋊Q8—22no—
191C22⋊Q8D4×C15114yes—
192C4×Q8—24no—
193C4×Q8—24no—
194C4×Q8—24no—
195C4×Q8—22no—
196C4×Q8—22no—
197C4×Q8C23×C15114yes—
198#117—22no—
199#117D4×C15112yes—
200C2×C42C23×C15111yescharacteristic
201C4⋊C8C23×C15114yes—
202#102—28no—
203#102—28no—
204C22⋊C8—22no—
205#97—21no—
206C4×C8—22no—
207C4×C8C23×C15112yes—
208C24—41no—
209C2×Q8—22no—
210C2×Q8—22no—
211C2×Q8C2×D4×C15114yes—
212C2×D4—22no—
213C2×D4—24no—
214C2×D4—44no—
215C2×D4—42no—
216C2×D4—41no—
217C2×D4—84no—
218C22×C4C2×D4×C15112yes—
219C22×C4C2×D4×C15111yescharacteristic
220SD16—88no—
221M16—42no—
222C2×C8—24no—
223C2×C8—22no—
224C4⋊C4—28no—
225C4⋊C4—28no—
226C4⋊C4—28no—
227C4⋊C4—22no—
228C4⋊C4—22no—
229C4⋊C4—22no—
230C4⋊C4—24no—
231C4⋊C4—24no—
232C4⋊C4—22no—
233C4⋊C4—24no—
234C4⋊C4C2×D4×C15114yes—
235C4⋊C4C2×D4×C15114yes—
236C22⋊C4—24no—
237C22⋊C4—22no—
238C42—28no—
239C42—22no—
240C42—24no—
241C42C2×D4×C15112yes—
242C42C2×D4×C15111yescharacteristic
243C42C24×C15111yescharacteristic
244C23—42no—
245C23—82no—
246C23—84no—
247C23#120×C15111yescharacteristic
248Q8—28no—
249Q8—44no—
250Q8—44no—
251D4—44no—
252D4—48no—
253D4—84no—
254D4—82no—
255C2×C4—22no—
256C2×C4—24no—
257C2×C4—24no—
258C2×C4—24no—
259C2×C4—24no—
260C2×C4#120×C15112yes—
261C2×C4#120×C15111yescharacteristic
262C2×C4C22×D4×C15111yescharacteristic
263C2×C4C22×D4×C15112yes—
264C8—42no—
265C8—44no—
266C22—22no—
267C22—21no—
268C22—84no—
269C22—82no—
270C22—164no—
271C22C2×#120×C15111yescharacteristic
272C4—22no—
273C4—21no—
274C4—44no—
275C4—44no—
276C4—44no—
277C4#454×C15112yes—
278C4#577×C15114yes—
279C2—41no—
280C2—162no—
281C2#3010×C15112yes—
282C2C2×#454×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#127×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #3556×C151C2semidirect
4. #1626×C151C2semidirect
5. #1544×C151C2semidirect
6. #1485×C151C2semidirect
10. #557×C151C22semidirect
25. #332×C151C22semidirect
26. Q8⋊C8×C151C22semidirect
141. #18731C151direct (N × H)
142. C151#18731direct (N × H)
143. #3556C2×C151semidirect
146. #1626C2×C151semidirect
147. #1544C2×C151semidirect
148. #1485C2×C151semidirect
152. #557C22×C151semidirect
167. #332C22×C151semidirect
168. Q8⋊C8C22×C151semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#3556×C1512
#3208×C1512
#3138×C1512
#1626×C1512
#1544×C1512
#1485×C1512
#18731151